Structural Health Monitoring (SHM)
Working document
1 Research Question:
How can sensor placement in structural health monitoring of buildings be optimized by minimizing expected maintenance decision cost rather than maximizing damage detectability?
note: shift form physics optimal monitoring -> decision optimal monitoring.
Sub Questions:
- How does sensor placement influence damage detection probability?
- How do detection errors propagate into maintenance decisions? (what are the costs of false positives and false negatives?)
- What is the economically optimal number and location of sensors?
- What are the optimal number and type of non-vibration sensors to detect the effect of non-damage related effects (like temperature, humidity, etc.) on the vibration data?
- When is SHM economically beneficial compared to periodic inspection?
more,
- Can information be weighted by consequence of failure? (consequence of failure by loss of element)
Not focusing on:
- Optimal Sensor data processing (onsite vs offsite)
- Optimal sensor type (vibration vs non-vibration)
1.1 Problem Formulation
1.1.1 Events / categories:
- \(S\) is the structural information (Stiffness, mass, geometry)
- \(D \in \{D_0, D_1, D_2, ..., D_k\}\)
- (D_0) = healthy
- (D_i) = damage at location (e.g. stiffness reduction)
- (D_0) = healthy
- \(L\) is load and environmental conditions acting on the structure (temperature, humidity, wind, etc.)
- \(x\) is an location on the structure
- \(a \in \{\text{Do nothing},\ \text{Inspect},\ \text{Repair}\}\)
Sensor are placed at locations \(x\), where the product measurements is given as \(y\). \[ y = f(S, D, L, x) + \varepsilon \]
A damage detection algorithm estimates: \[ P(D_i | y) \]
Cost of decision \(a\) given damage state \(D_i\) is given as \(C(a, D_i)\).
| Decision | Healthy | Damaged |
|---|---|---|
| Do nothing | 0 | Failure risk |
| Inspect | Inspection cost | Inspection cost |
| Repair | Unnecessary repair | Repair cost |
note: this can be expanded to include false positives and false negatives, and the cost of these errors.
Expected decision cost: \[ \mathbb{E}[C | y] = \sum_{i} C(a, D_i) P(D_i | y) \]
1.1.2 Objective: Optimization Problem
chosen number and location of sensors \(x\) to minimize expected decision cost: \[ \boxed{ x^* = \arg\min_x \mathbb{E}[C_{total}(x)] } \]
where total cost includes:
\[ C_{total} = C_{sensors} + C_{false\ alarms} + C_{missed\ damage} + C_{inspection} \]
Expanded:
\[ \mathbb{E}[C_{total}] = C_{install}(x) \cdot P(FP|x)C_{FP} \cdot P(FN|x)C_{FN} \]
2 Focused Literature Review (week 2)
2.1 General
2.2 Introduction of damage to the structure (D)
2.2.1 Paper 1
Rosafalco et al. (2021), PDF, (reading: skim)
- there are 2 SHM main approaches:
- “SHM model model-based”: the update of a numerical model (e.g. through Kalman flters or optimization) [1]
- Have an hard time whit dealing whit the noise in the data
- Have an hard time whit dealing whit the noise in the data
- “SHM data-driven”: the use of data to directly estimate damage state (e.g. through machine learning) [2]
- Supervised learning - ML, labelled data, damage state is known
- Unsupervised learning - ML, unlabelled data, damage state is unknown
- “Simulation-Based Classification (SBC)” - an hybrid approach, labeled data is created form FEM model [3]
- need to take varying operational and environmental conditions into account (e.g. temperature, humidity, load, etc.)
- “SHM model model-based”: the update of a numerical model (e.g. through Kalman flters or optimization) [1]
2.3 Vibration-based SHM
note: this is both for model model-based and data-driven methods for damage detection.
2.3.1 Paper 1
Sun et al. (2023), PDF, (paper type: review, reading: detailed)
note: Comments on strengths and weaknesses for each of the 5 methods are given (use them).
- Vibration-based damage identification methods: [1]
- natural frequency-based [section 2]
- hard to distinguish between damage and environmental effects [3]
- is an example “how to optimize the sampling interval to minimize the effects of measurement noise requires further research.” [4] and [section 2.2] (validates my research question)
- mode shape-based [section 3] and modal curvature-based [section 3.2]
- can be used to localize damage
- ref to 2 papers where they try to use fever sensors to estimate the mode shapes [5]
- ref to one paper where they down sampled the frequency whiteout losing mode shape [6]
- sensitive to noise and environmental effects [7], [9]
- large number of measurement points are needed to accurately estimate mode shapes [8]
- many papers after [9]
- Methods Based on Modal Strain Energy - combined methods based on both frequencies and mode shapes. [Section 4]
- 2 stage model(in many cases): [10]
- Damage is localized in the first stage by an damage index divided through strain energy, [10]
- and then the severity of the damage is estimated in the second stage by an optimization optimization algorithms. [10]
- (note there are references to may papers there cut be of relevance in the end of page 19)
- Ref. to paper there uses PCA (Principal Component Analysis) - to uncouple collated variables like temperature and damage [11]
- computationally expensive, for structures whit many elements [12]
- If error in step 1 then can not be corrected in step 2 [13]
- 2 stage model(in many cases): [10]
- Methods Based on Modal Flexibility [section 5]
- one study shows that the “Methods Based on Modal Flexibility” preform vers when many sensors are used, compared to “Methods curvature based method”, but it is not that sensitive to small damages? [14]
- an real case study whit temperatures effects on stiffness [15]
- they conclude that only the first couple of modes are needed to estimate the flexibility matrix and there for is there an need for fewer sensors [16]
- they conclude that the flexibility based method is not good for damage severity [17]
- machine learning / data-driven methods / statistical methods [2]
- they are strong and can be used to filter out the noise and environmental effects, but if there is used supervised learning then there is a need for labeled data, which need much compute (note this is not based on this paper but is an general observation)
- natural frequency-based [section 2]
